Critical Fidelity

Details Critical Fidelity Critical Fidelity

2006-08-25

arxiv.org/abs/cond-mat/0608555v2

Phys. Rev. Lett. 97, 256404 (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 3 figures. Revised and published in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.97.256404

Using a Wigner Lorentzian Random Matrix ensemble, we study the fidelity, $F(t)$, of systems at the Anderson metal-insulator transition, subject to small perturbations that preserve the criticality. We find that there are three decay regimes as perturbation strength increases: the first two are associated with a gaussian and an exponential decay respectively and can be described using Linear Response Theory. For stronger perturbations $F(t)$ decays algebraically as $F(t)\sim t^{-D_2}$, where $D_2$ is the correlation dimension of the critical eigenstates.

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